Tooth enamel is composed of hydroxyapatite, whose simplest formula is Ca5(PO4)3OH, and whose corresponding 𝐾𝑠𝑝=6.8×10−27. As discussed in the “Chemistry and Life” box on “Tooth Decay and Fluoridation” in Section 17.5, fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, Ca5(PO4)3F, whose 𝐾𝑠𝑝=1.0×10−60. a. Write the expression for the solubility-constant for hydroxyapatite and for fluoroapatite.
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Identify the chemical formulas for hydroxyapatite and fluoroapatite: Ca_5(PO_4)_3OH and Ca_5(PO_4)_3F, respectively.
Understand that the solubility product constant (K_sp) is the equilibrium constant for the dissolution of a solid substance into its constituent ions in a saturated solution.
Write the dissolution equation for hydroxyapatite: Ca_5(PO_4)_3OH (s) ⇌ 5 Ca^{2+} (aq) + 3 PO_4^{3-} (aq) + OH^- (aq).
Write the K_sp expression for hydroxyapatite: K_{sp} = [Ca^{2+}]^5 [PO_4^{3-}]^3 [OH^-].
Write the dissolution equation and K_sp expression for fluoroapatite: Ca_5(PO_4)_3F (s) ⇌ 5 Ca^{2+} (aq) + 3 PO_4^{3-} (aq) + F^- (aq); K_{sp} = [Ca^{2+}]^5 [PO_4^{3-}]^3 [F^-].
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solubility Product Constant (Ksp)
The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced dissolution equation. For example, for hydroxyapatite, the Ksp expression would involve the concentrations of calcium and phosphate ions. A lower Ksp value indicates lower solubility.
Dissolution equilibrium refers to the dynamic balance between the solid phase of a compound and its ions in solution. When a solid dissolves, it breaks into its constituent ions, which then enter the solution. At equilibrium, the rate of dissolution equals the rate of precipitation, allowing for the calculation of Ksp. Understanding this concept is crucial for writing Ksp expressions for compounds like hydroxyapatite and fluoroapatite.
The chemical reaction of fluoridation involves the substitution of hydroxide ions in hydroxyapatite with fluoride ions to form fluoroapatite. This reaction not only alters the solubility properties of the compound but also enhances its resistance to decay. The Ksp of fluoroapatite is significantly lower than that of hydroxyapatite, indicating that fluoroapatite is less soluble and thus more stable in the presence of fluoride, which is important for dental health.
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